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Thermodynamic scaling of dynamics in polymer melts: Predictions from the generalized entropy theory
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10.1063/1.4809991
/content/aip/journal/jcp/138/23/10.1063/1.4809991
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/23/10.1063/1.4809991

Figures

Image of FIG. 1.
FIG. 1.

The logarithm of relaxation time log (τ) calculated from the generalized entropy theory as a function of the ratio ϕ/ with γ = 14.0 for various pressures. The computations are performed for a melt of chains with the structure of poly(propylene) (PP) with = 6, = 2.7 Å, ε/ = 200 K, / = 400 K, and = 8000. The same values of , , ε, , and are used in the computations presented in Fig. 2 . τ is given in units of seconds, which is also used in Fig. 4 . Thermodynamic scaling holds well for low pressures, but relaxation times for ≳ 50 MPa deviate from the master curve.

Image of FIG. 2.
FIG. 2.

The logarithm of glass transition temperature log ( ) as a function of the logarithm of glass transition specific volume log ( ). The red solid line is a linear fit to the data of slope 13.47 for ⩽ 50.7 MPa. A linear relationship between log ( ) and log ( ) indicates that the relaxation times obey thermodynamic scaling.

Image of FIG. 3.
FIG. 3.

Specific volumes as a function of temperature for various pressures. The symbols are experimental data taken from Ref. for atactic PP with high molecular weight, and the lines are results calculated from the generalized entropy theory for a melt of chains with the PP structure with = 6, / = 409 K, and = 8000. The cell volume parameter and cohesive energy ε are adjusted to decrease with pressure in order to better describe the experimental data. The parameters are summarized in Table I .

Image of FIG. 4.
FIG. 4.

(a) The logarithm of relaxation time log (τ) as a function of the ratio ϕ/ for various . (b) The logarithm of glass transition temperature log ( ) as a function of the logarithm of glass transition specific volume log ( ) for various . The solid lines in (b) are linear fits. The computations are performed for the PP structure with = 6, = 2.7 Å, ε/ = 200 K, and = 8000. The same values of , , ε, and are used in the computations presented in Figs. 5 and 7 .

Image of FIG. 5.
FIG. 5.

Scaling exponents γ, estimated from two independent methods, as a function of bending energy . The red squares and blue circles are obtained from relaxation times and Eq. (2) , respectively.

Image of FIG. 6.
FIG. 6.

Scaling exponents γ as a function of side group bending energy for various fixed backbone bending energies . The calculations consider a poly(1-pentene) (PPe) structure with = 6, = 2.7 Å, ε/ = 200 K, and = 8000.

Image of FIG. 7.
FIG. 7.

(a) Isochoric fragility parameter as a function of bending energy . (b) The product of isobaric expansion coefficient α at the glass transition point and glass transition temperature as a function of bending energy at constant pressure ( = 0.1 MPa). The lines are a guide to the eye.

Image of FIG. 8.
FIG. 8.

Scaling exponent γ and isochoric fragility parameter as a function of cohesive energy ε. The computations are performed for a polymer melt with the PP structure with = 6, = 2.7 Å, / = 400 K, and = 8000.

Image of FIG. 9.
FIG. 9.

Scaling exponent γ and isochoric fragility parameter as a function of chain length . The computations are performed for a polymer melt with the PP structure with = 6, = 2.7 Å, ε/ = 200 K, and / = 400 K. The smallest value for is 8.

Image of FIG. 10.
FIG. 10.

Scaling exponent γ and isochoric fragility parameter as a function of side group length . The computations are performed for the poly(α-olefin) structure with = 6, = 2.9 Å, ε/ = 200 K, K, K, and = 8000.

Image of FIG. 11.
FIG. 11.

Correlations between isobaric fragility parameter at = 0.1 MPa and isochoric fragility parameter when varying individual molecular parameters. The lines are a guide to the eye.

Image of FIG. 12.
FIG. 12.

Correlations between scaling exponent γ and isochoric fragility parameter when varying individual molecular parameters. The lines are linear fits according to Eq. (6) with the fitting parameters, γ = −8.65 and = 847 for chains with the poly(propylene) structure, γ = −10.54 and = 852 for poly(1-pentene), γ = −4.52 and = 616 for poly(α-olefin).

Tables

Generic image for table
Table I.

Cell volume parameters , cohesive energies ε, calculated glass transition temperatures , and experimental glass transition temperatures for various pressures. Using the pressure dependent and ε along with the bending energy / = 409 K produces the calculated pressure dependence of the glass transition temperature in good agreement with experimental one.

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/content/aip/journal/jcp/138/23/10.1063/1.4809991
2013-06-17
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Thermodynamic scaling of dynamics in polymer melts: Predictions from the generalized entropy theory
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/23/10.1063/1.4809991
10.1063/1.4809991
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